Approximate addition is a technique to trade off energy consumption and output quality in error-tolerant applications. In prior art, bit truncation has been explored as a lever to dynamically trade off energy and quality. In this brief, an innovative bit truncation strategy is proposed to achieve more graceful quality degradation compared to state-of-the-art truncation schemes. This translates into energy reduction at a given quality target. When applied to a ripple-carry adder, the proposed bit truncation approach improves quality by up to 8.5 dB in terms of peak signal-to-noise ratio, compared to traditional bit truncation. As a case study, the proposed approach was applied to a discrete cosine transform engine. In comparison with prior art, the proposed approach reduces energy by 20%, at insignificant delay and silicon area overhead.
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A scalable approximate multiplier, called truncation- and rounding-based scalable approximate multiplier (TOSAM) is presented, which reduces the number of partial products by truncating each of the input operands based on their leading one-bit position. In the proposed design, multiplication is performed by shift, add, and small fixed-width multiplication operations resulting in large improvements in the energy consumption and area occupation compared to those of the exact multiplier. To improve the total accuracy, input operands of the multiplication part are rounded to the nearest odd number. Because input operands are truncated based on their leading one-bit positions, the accuracy becomes weakly dependent on the width of the input operands and the multiplier becomes scalable. Higher improvements in design parameters (e.g., area and energy consumption) can be achieved as the input operand widths increase. To evaluate the efficiency of the proposed approximate multiplier, its design parameters are compared with those of an exact multiplier and some other recently proposed approximate multipliers. Results reveal that the proposed approximate multiplier with a mean absolute relative error in the range of 11%–0.3% improves delay, area, and energy consumption up to 41%, 90%, and 98%, respectively, compared to those of the exact multiplier. It also outperforms other approximate multipliers in terms of speed, area, and energy consumption. The proposed approximate multiplier has an almost Gaussian error distribution with a near-zero mean value. We exploit it in the structure of a JPEG encoder, sharpening, and classification applications. The results indicate that the quality degradation of the output is negligible. In addition, we suggest an accuracy configurable TOSAM where the energy consumption of the multiplication operation can be adjusted based on the minimum required accuracy.
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